Weighted Random Walk (WRW) is RW on a weighted graph [1]}. At node \(u\) , WRW chooses the edge \(\lbrace u,v\rbrace \)  to follow with probability \(P_{u,v}\)  proportional to the weight \(\textrm {w}(u,v)\ge 0\)  of this edge, i.e., 
\(P_{u,v}=\frac{\textrm {w}(u,v)}{\sum _{v^{\prime }\in \mathcal {N}(u)} \textrm {w}(u,v^{\prime })}.\) 
